Best Known (46, 46+16, s)-Nets in Base 16
(46, 46+16, 16384)-Net over F16 — Constructive and digital
Digital (46, 62, 16384)-net over F16, using
- net defined by OOA [i] based on linear OOA(1662, 16384, F16, 16, 16) (dual of [(16384, 16), 262082, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(1662, 131072, F16, 16) (dual of [131072, 131010, 17]-code), using
- trace code [i] based on linear OA(25631, 65536, F256, 16) (dual of [65536, 65505, 17]-code), using
- an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- trace code [i] based on linear OA(25631, 65536, F256, 16) (dual of [65536, 65505, 17]-code), using
- OA 8-folding and stacking [i] based on linear OA(1662, 131072, F16, 16) (dual of [131072, 131010, 17]-code), using
(46, 46+16, 71096)-Net over F16 — Digital
Digital (46, 62, 71096)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(1662, 71096, F16, 16) (dual of [71096, 71034, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(1662, 131072, F16, 16) (dual of [131072, 131010, 17]-code), using
- trace code [i] based on linear OA(25631, 65536, F256, 16) (dual of [65536, 65505, 17]-code), using
- an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- trace code [i] based on linear OA(25631, 65536, F256, 16) (dual of [65536, 65505, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(1662, 131072, F16, 16) (dual of [131072, 131010, 17]-code), using
(46, 46+16, large)-Net in Base 16 — Upper bound on s
There is no (46, 62, large)-net in base 16, because
- 14 times m-reduction [i] would yield (46, 48, large)-net in base 16, but